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Hitting the Nail [Was: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)]
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tmichael  
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 More options 12 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: tmich...@worldnet.fr
Date: 1998/05/12
Subject: Hitting the Nail [Was: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)]

On 9 May 1998 21:11:00 GMT, in humanities.philosophy.objectivism Jim

Klein  <rum...@ix.netcom.com> wrote:
>In <6j2d6c$3d...@nntp2.ba.best.com> "Samantha Atkins"
><saman...@theLove.org> writes:
>   Remember,  reality is always
>>the final arbiter.   Your philosophy cannot chuck out reality without
>>invalidating itself.    Reality is the foundation of philosophy, not
>>the other way around.
>Oh, what a mouthful there...thank you!  Believe it or not, that's about
>ALL I've been trying to say for about two years now, at least on the
>topic of why I think the ARI has abandoned Objectivism.  You've said it
>far more clearly, with about 1/100,000 the verbiage and none of the
>caustic bite.

Dear Jim,

You're quite right of course. What Samantha Atkins said was a real
mouthful. Brief, concise and to the point.

Whether you are aware of it or not you HAVE been saying the same thing
yourself for quite some time though not in exactly the same way. At
least from my way of reading you.

>Objectivism as a philosophy MUST adhere (adjust, conform) to reality,
>or it automatically invalidates itself.  What a concept...nice job!
>jk

Having said this my chief problem is do I see and understand reality
as it is ?

If there can be one reality for you - or anybody else -  and another
for me then that gives us two different philosophies.

Since even the most briliant of human minds has its limits then this
is easily conceivable.

Of course there can only be ONE ABSOLUTE reality which doesn't really
solve the problem since we are probably both convinced that we, you or
I, have the true reality.

Another thing I've been meaning to ask you for quite some time: what
is ARI ? The Ayn Rand Institute perhaps ? And why is it so important ?
Is it the official mouthpiece of Objectivism ?

Thanks a lot, Kindest regards, Michael Thackray


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Jim Klein  
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 More options 12 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: Jim Klein <rum...@ix.netcom.com>
Date: 1998/05/12
Subject: Re: Hitting the Nail [Was: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)]

In <3558adbe.1278...@mailhost.worldnet.fr> tmich...@worldnet.fr writes:
>Having said this my chief problem is do I see and understand reality
>as it is ?

Yes and probably.

>If there can be one reality for you - or anybody else -  and another
>for me then that gives us two different philosophies.

There CAN'T be one reality for one person, and another for another.
There may only be different interpretations of the same reality.
That's why Objectivism is built on the primacy of existence, rather
than the primacy of consciousness.  The former leaves a possible way
out;  the latter doesn't.

>Since even the most briliant of human minds has its limits then this
>is easily conceivable.

Literally, it's not conceivable.  What's conceivable is to switch the
meaning of certain words--like "reality" or "existence"--and devise
fantasies which render them as alterable through consciousness.

The fact that even the most brilliant of minds may differ on their
understanding of reality, does not affect the fact that the reality
itself stays the same.

>Of course there can only be ONE ABSOLUTE reality which doesn't really
>solve the problem since we are probably both convinced that we, you or
>I, have the true reality.

That's true---it doesn't solve the problem of knowing what that actual
reality is, but it DOES solve the problem of trying to figure out
whether it actually exists.

>Another thing I've been meaning to ask you for quite some time: what
>is ARI ? The Ayn Rand Institute perhaps ?

Yes.

>And why is it so important ?

It's important because it has a very large influence both on how
Objectivism is perceived by non-Objectivists, and even more importantly
on how Objectivism is represented to those who find Rand's novels very
appealing and meaningful.

The ARI gets "first crack" through two means, neither of which are
built on their own accomplishments.  First, there's those silly green
cards prominently placed in the novels.  Don't get me wrong---they own
the rights, and are free to try to get "customers" any way they want.
If it were me though, I'd do it much less conspicuously, thus allowing
the words of Rand to have greater prominence than the ad.  Long before
I knew anything about the "Objectivist movement," I was hesitant at
even giving away copies of her books, since the cards in the middle are
the first thing noticed, and make it readily appear that the books are
part of some cult movement.  I doubt that I'm alone in this, which
means that there are plenty of people who have not read Rand that might
have, had others not wished to appear so cult-like.  OTOH, there are
surely contributors to the ARI who wouldn't have been, had the cards
not been thicker than the pages of the book and in the middle.  I guess
it's just a question of priorities.  [Though I'd like to hear Betsy
explain why the ARI would want THOSE "customers" anyway!]

Then there's the fact that a web-search of "Ayn Rand" or a peek at the
most public FAQs will inevitably direct one to the ARI website.  Also,
there's the question of various ARI-oriented organizations sharing
mailing lists, even without notifying the people on the list.  Both of
these factors build heavily upon the fact that many ARIans, even when
pretending to objectively discuss Objectivism, conveniently ignore
(read: evade) the fact that non-ARI Objectivist organizations exist.
Yeah, I know...it's a "question of sanction."  What isn't, to the ARI?

Thankfully, the web factor has greatly declined over the past few
years, with the development of "The Objectivist Ring" and gaining
prominence of the IOS and other Objectivist organizations.

Again, none of this is blatantly immoral or illegal;  I'm just trying
to explain HOW the ARI has gained such importance in the Objectivist
movement.  The fact that Rand made a SECOND error at trying to name
someone her "intellectual heir" didn't help matters either.  You should
hear what some ARIans have to say about her first "intellectual heir!"
Apparently, they're of the opinion that the same action can be a
terrible mistake one day, and a magnificent feat the next.

As to how the ARI has greatly MISUSED its position...well, I've gone
into pretty extensive detail on that;  I'll give it a break this trip.

>Is it the official mouthpiece of Objectivism ?

Yeah, like Bill Clinton is the official mouthpiece for the American
Ideal.  JUST like that, in fact!

jk


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Discussion subject changed to "Rand and Infinity (Was: Re: Rand & Von Neumann....)" by Mark A. Peters
Mark A. Peters  
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 More options 13 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: "Mark A. Peters" <Mark.A.Pet...@cdc.com>
Date: 1998/05/13
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

Philosophy as such _is_ the foundation for all science, whether or not any
particular philosophy contains errors.  In Objectivism, the law of identity
_is_ an axiom, and it's all you need to know to refute claims about anything
actually being infinite.

To use discoveries by science as "an important" check is fine, but it isn't
necessary.  All you need to _prove_ a philosophy true is what you can get
using your own unaided senses, and your own mind.  You don't need the
specialized machines and tools of science.  And as I said, _no_ scientific
discovery could _ever_ prove that any actual thing is infinite.  That's
because doing so would invalidate the law of identity, which is a principle
upon which science depends.  Invalidate the law of identity with science,
and you invalidate the science (and all other knowledge) in the same
instant.

Reality certainly is the foundation of philosophy - but then I never claimed
otherwise.

Mark Peters


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GRADinc  
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 More options 14 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: GRADinc <grad...@aol.com>
Date: 1998/05/14
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

Mark A. Peters

>  In Objectivism, the law of identity
>_is_ an axiom, and it's all you need to know to refute claims about anything
>actually being infinite.

Except you are misapplying the axiom if you conclude
that the universe cannot be infinite.

>To use discoveries by science as "an important" check is fine

So what will you do if this check finds evidence of an infinite
universe?

Tom Clarke


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Samantha Atkins  
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 More options 14 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: "Samantha Atkins" <saman...@theLove.org>
Date: 1998/05/14
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

Les wrote:

>Depending on the total mass of the universe, there
>are three outcomes:

>1) Gravity exceeds the expansion, leading to a "Big Crunch".

>2) The mass is "just right", so that the universe
>reaches a finite, constant size.

>3) The universe expands forever.

>If 3) is the case, and no other fundamental limit is
>reached, then time would be open-ended, and there
>would be no upper limit on the size of the universe.

Ah.  But at any particular time, T, after the Big Bang, the universe is
guaranteed to be at a finite size.   This was all I was trying to assert.

- samantha


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Samantha Atkins  
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 More options 14 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: "Samantha Atkins" <saman...@theLove.org>
Date: 1998/05/14
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

Mark A. Peters wrote in message <6jd8u7$dk...@cdshub.cdc.com>...
>Philosophy as such _is_ the foundation for all science, whether or not any
>particular philosophy contains errors.  In Objectivism, the law of identity
>_is_ an axiom, and it's all you need to know to refute claims about
anything
>actually being infinite.

Can you please illustrate what precisely about the law of identity actually
mandates that an existent cannot be of infinite size,  in the sense of being
immeasurable and uncountable much like the simple infinity of the natural
numbers in mathematics?   The universe, while of finite size at any moment,
can be argued with some justification to be of countably infinite extent.

A question I don't know how to approach with my limited scientific
knowledge:   In the infinite gravity well of a black hole wouldn't the
acceleration due to gravity be infinite and thus would not velocities far in
excess of a mere finite value like c, the speed of light,   be attainable?
Just a curious question way too late at night.

- samantha


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Robert Kolker  
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 More options 14 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: Robert Kolker <r...@tiac.net>
Date: 1998/05/14
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

Samantha Atkins (saman...@theLove.org) wrote:

.......................snip..............................

> Can you please illustrate what precisely about the law of identity actually
> mandates that an existent cannot be of infinite size,  in the sense of being
> immeasurable and uncountable much like the simple infinity of the natural
> numbers in mathematics?   The universe, while of finite size at any moment,
> can be argued with some justification to be of countably infinite extent.

        I think not. Countably infinite referes to the cardinality
        of a set of objects that can be put in one to one correspondence
        with the set of integers. Are there infinitely many of any
        kind of thing in the physical cosmos? I have seen no evidence
        to that effect.

        Bob Kolker


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GRADinc  
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 More options 14 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: GRADinc <grad...@aol.com>
Date: 1998/05/14
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

Samantha Atkins

>But at any particular time, T, after the Big Bang, the universe is
>guaranteed to be at a finite size.  

Not true.  If the universe is bigger than any finite size,
then it will always have been bigger than any finite size.
At any time the observable universe is finite.

Think of the big bang not as the time when the universe's
size approaches zero, but as the time at which the universe's
density tends to exceed any finite value.

Tom Clarke

P.S.  In this post I have avoided the I-word, using instead
the mathematicians definitions underlying their use of the
I-word.


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GRADinc  
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 More options 14 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: GRADinc <grad...@aol.com>
Date: 1998/05/14
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

Robert Kolker

>Are there infinitely many of any
>kind of thing in the physical cosmos? I have seen no evidence
>to that effect.

Since you are a finite being you will never see such evidence.
However, using your mind you could identify evidence that
contradicted the finiteness of the cosmos.

Tom Clarke


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DSANDIN  
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 More options 14 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: DSANDIN <dsan...@aol.com>
Date: 1998/05/14
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

GRADinc <grad...@aol.com> (Tom Clarke) wrote:
   Date: Thu, May 14, 1998 08:34 EDT
   Message-id: <1998051412334800.IAA23...@ladder01.news.aol.com>

>Robert Kolker

>>Are there infinitely many of any
>>kind of thing in the physical cosmos? I have seen no evidence
>>to that effect.

>Since you are a finite being you will never see such evidence.
>However, using your mind you could identify evidence that
>contradicted the finiteness of the cosmos.

Each of your two sentences is specific and not subject to
multiple interpretations.  And they utterly contradict each other.

"Being finite, you will never do A"  plus  "You could do A",
where A = "identify evidence contradicting finiteness".

--- Dean


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GRADinc  
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 More options 14 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: GRADinc <grad...@aol.com>
Date: 1998/05/14
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

DSANDIN

>>Since you are a finite being you will never see such evidence.
>>However, using your mind you could identify evidence that
>>contradicted the finiteness of the cosmos.
>Each of your two sentences is specific and not subject to
>multiple interpretations.  And they utterly contradict each other.

No they don't.  You are just thinking too narrowly,
but I think I may not have been precise enough, as well.
Let me be even more specific and give some examples
of evidence that a human could identify that would
contradict finiteness of the cosmos.

If the universe is finite then as observations are made at
larger and larger distances there are definite consequences
for the number of galaxies observed (the number will decrease).
Imagine trying to find out whether the earth if finite (spherical)
or not finite (flat) by counting the trees at a given distance from
your house.  Assuming that trees grow at a constant density,
you will find that the number of trees at 100 miles will be less
to times the number of trees at 10 miles distance because of
the curvature of the earth.  Astronomers do the same thing
with stars.  If they find that the number of galaxies at 100 billion
light years are 10 times thenumber at 10 billion light years
then they can say (identify) that the size of the universe
is greater than thus and so size.  
This process could be repeated with greater precision or
at greater distances to conclude that the universe is even
bigger still.

So I should have said
For any given value of the size of the universe, using your
mind you could identify evidence that shows the universe
is bigger than that value.

Returning to your statement:

>"Being finite, you will never do A"  plus  "You could do A",
>where A = "identify evidence contradicting finiteness".

In my first statement, A="infinitely many of any kind of physical
thing".

In my second statement A= "identify evidence contradicting finiteness", as you
say.

Note that the first explicity includes "infinite" the second
does not.
To more precise version of my second statement has
A="identify evidence contradicting any specific value of the
size of the cosmos".

I am going to take a different tack from now on in
my battle to convince Objectivists of the consistency
of actual infinity with A=A.  
I will  not mention infinity explicity and only speak of
finite things.
This is actually the great discovery of Cantor and other
19/early 20th century mathematicians.  That you can
make use of the concept of infinity without actually
talking about it.

A purely mathematical example is the Dirac delta function.
This is a very useful "fictional" function.  A physical
circuit like an amplifier has a think called an impulse
response that when convolved with the input signal
gives the output signal.  Calculationally it is convenient
to have an impulse response for the ideal perfect amplifer -
the mythical amplifying piece of wire that audiophiles speak of.
Such an impulse response would be Dirac's delta function,
a function with a value of infinity at zero time and a value
of zero everywhere else.
Well engineers and physicists seized on this impossible
function and used it for years to design and analyze real
things with great success.
Mathematicians were horrified.  No function can have
an infinite value at a point.  So they rolled up their sleeves
and defined the delta function in terms of a sequence of
ordinary finite functions. each function in the sequence more
peaked and more narrow than the last.  Using such
sequences they proved that the delta function sequence
behaved just like the impossible infinite valued function
that Dirac thought up.

So in Objective terms the delta function is a concept of
method.  It is also the impulse response of a piece of wire
so in a sense it is an existent.

If you are still with me.  I think the difference is
epistemology versus ontology.
If A=ontologically infinite then not A=ontologically finite.
if B=evidence for infinititude is impossible
but not B=evidence for finiteness is  possible.

Since existence is primary I don't see how the
limitations of epistemology can constrain ontology.

Tom Clarke


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Discussion subject changed to "Hitting the Nail [Was: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)]" by Stephen Grossman
Stephen Grossman  
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 More options 14 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: Stephen Grossman <sdgr...@att.net>
Date: 1998/05/14
Subject: Re: Hitting the Nail [Was: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)]

In article <6j2gon$...@sjx-ixn11.ix.netcom.com>, Jim Klein

<rum...@ix.netcom.com> wrote:
> In <6j2d6c$3d...@nntp2.ba.best.com> "Samantha Atkins"
> <saman...@theLove.org> writes:

> >Mark Peter's writes:

 >>Philosophy is the foundation of science, not the other way around.

Yes!

> >Assuming that one's philosophy is in fact correct.  

No, even a false philosophy grounds, in a false way, science. Each
philosophy causes a particular science. Eg, Materialism causes
behaviorism. Aristotles philosophy caused classical science. Kants
philosophy caused scientific relativism, subjectivism, skepticism. Eg,
Aristotle's philosophy, w/its metaphysics of identity and causality, did
not cause QM physics.

>>However,
> >mistakes could have been made at any stage of philosophical reasoning
> >beyond the base axioms.

Philosophical error causes scientific error.

 >> Thus the actual evidence found in reality

> >through science is an important  check.

Youre begging the question of the metaphysical and epistemological status
of scientific observation. All science is an application of some
philosophy.

> Objectivism as a philosophy MUST adhere (adjust, conform) to reality,
> or it automatically invalidates itself.

Obj conforms to reality as objectively understood, not as subjectively felt.
€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€
I fought the Logos and the Logos won. ODYSSEUS
...the silly dead... HOMER
Reason is man's basic means of survival.  AYN RAND
--------------------------------------------------------------------------- --
Tracking Marxist dialectical revolution: ZigZag
Radically systematic radical metaphysics: Existence 2
http://home.att.net/~sdgross
--------------------------------------------------------------------------- -
Stephen Grossman        
Fairhaven, MA, USA      
sdgr...@att.net      
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GRADinc  
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 More options 14 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: GRADinc <grad...@aol.com>
Date: 1998/05/14
Subject: Re: Hitting the Nail [Was: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)]

Stephen Grossman

claims to hit the nail

>Obj conforms to reality as objectively understood, not as subjectively felt.

So Objectivisim dictates to reality through the
process of Objective understanding?
So much for primacy of existence!!

Tom Clarke


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Discussion subject changed to "Rand and Infinity (Was: Re: Rand & Von Neumann....)" by Mark A. Peters
Mark A. Peters  
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 More options 14 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: "Mark A. Peters" <Mark.A.Pet...@cdc.com>
Date: 1998/05/14
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

Samantha Atkins wrote in message <6jeibq$cb...@nntp2.ba.best.com>...
>Mark A. Peters wrote in message <6jd8u7$dk...@cdshub.cdc.com>...
>>[...]
>Can you please illustrate what precisely about the law of identity actually
>mandates that an existent cannot be of infinite size,  in the sense of
being
>immeasurable and uncountable much like the simple infinity of the natural
>numbers in mathematics? [...]

This has been done in this newsgroup about a thousand times, and it's been
done by Leonard Peikoff in OPAR far better than I'll do here.

The law of identity says that everything (every entity, attribute, etc.) is
what it is, is something specific, something definite.  To be is to be
_something_ - you cannot have the "it" without the "is" (or vice versa) in
"it is".  Existence and identity are not two separate facts, but two
different perspectives on the same fact.  The "is" in "it is" differentiates
a thing from nothing, while the "it" differentiates the thing from other
things.

To claim that the size of something (for example) is infinite is to say that
no matter what specific size you name, the thing in question is bigger.
Used in this sense, "infinity" is not a number, it is not specific, not
definite - i.e., it is a quantity with no _identity_, which is a violation
of the law of identity, and hence impossible.  Put another way, such a claim
is an attempt to say about a thing's size that "it is" without the "it".

Mark Peters


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Discussion subject changed to "Hitting the Nail [Was: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)]" by Samantha Atkins
Samantha Atkins  
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 More options 14 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: "Samantha Atkins" <saman...@theLove.org>
Date: 1998/05/14
Subject: Re: Hitting the Nail [Was: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)]

Michael Thackery writes:

>Having said this my chief problem is do I see and understand reality
>as it is ?

>If there can be one reality for you - or anybody else -  and another
>for me then that gives us two different philosophies.

There cannot be different realities for you and me.  There can be different
perceptions and understanding of the underlying reality.   Man's mode of
knowledge is not by nature free of all possibility of error.  Knowledge is
contextual;  it depends on the context of one's past thinking, the facts at
one's disposal and the care with which one thinks.   These factors are  just
a brief survey of the context.   Mistakes can be made in the process of
understanding reality.   That is why a common, objective reality and letting
that reality be the final arbiter in all disagreements between men is
essential.   Without a common objective reality there is no meaning in
talking of correct or incorrect.  Correct or incorrect with reference to
what?  Without a common objective reality there would be no way of reaching
any rational agreement or for supporting any conclusion (human rights for
example).  If you and I disagreed we would have no choice but to leave each
other severely alone and if that were not possible then we would have no
choice but to come to blows to settle our disagreement.

Besides honest errors one can practice evasion and the refusal to know.  One
can also have greatly wrecked (or had wrecked by the culture) one's
conceptual machinery and have a substantial job of rebuilding to do.

>Since even the most briliant of human minds has its limits then this
>is easily conceivable.

DIsagreement is conceivable.  Different realities is not.

>Of course there can only be ONE ABSOLUTE reality which doesn't really
>solve the problem since we are probably both convinced that we, you or
>I, have the true reality.

Hardly.  Relaity is not a possession but the axiomatic basis of our very
being.   I am only able to know whether I have done my honest best to
apprehended reality in specific matters that are of concern to me.  I can
know the level of my integrity, in other words, but I cannot know in some
impossible mystical absolute fashion that my conclusions are utterly correct
now and forever.   Within this context though I can know with all the
certainty that is in fact  possible to human beings.

>Another thing I've been meaning to ask you for quite some time: what
>is ARI ? The Ayn Rand Institute perhaps ? And why is it so important ?
>Is it the official mouthpiece of Objectivism ?

Sometimes I have the paranoid idea that those out to destroy Objectivism
have hit upon the excellent strategy of pretending to be its strongest
defenders.   From that position they then proceed to establish seemingly
logical but utterly wrong philosophical positions.  They defend these
positions as being not subject to testing by reality and even condemn all
those with the wit to follow the argument who disagree as being immoral(!?).
These positions turn off the most promising minds that are attracted to
Objectivism and over time leave mostly only the sheep.   This appears to
happen regardless of whether or not some person or group is at the heart of
it.   But yes,  ARI is as close to an "official" voice of Objectivism as we
have today.

- samantha


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Discussion subject changed to "Rand and Infinity (Was: Re: Rand & Von Neumann....)" by GRADinc
GRADinc  
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 More options 14 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: GRADinc <grad...@aol.com>
Date: 1998/05/14
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

Mark A. Peters

>The law of identity says that everything (every entity, attribute, etc.) is
>what it is, is something specific, something definite.

I think the mistake is in the "attribute etc".
Everthing that exists is certainly something definite,
but when you speak or attributes you cross into the
area of man's limited knowledge and perceptions, into
epistemology.

>To claim that the size of something (for example) is infinite is to say that
>no matter what specific size you name, the thing in question is bigger.

Excellent definition.  Fancied up a bit with symbols this
would go well in any math book.

>Used in this sense, "infinity" is not a number, it is not specific, not
>definite - i.e., it is a quantity with no _identity_,

Yes it is not a number in the sense of counting on your toes,
but you have just defined it very precisely.  That is its
identity.

>which is a violation
>of the law of identity, and hence impossible.  Put another way, such a claim
>is an attempt to say about a thing's size that "it is" without the "it".

If the universe is infinite, the "it" is the universe.
I still don't see the  problem.

Tom Clarke


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Samantha Atkins  
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 More options 15 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: "Samantha Atkins" <saman...@theLove.org>
Date: 1998/05/15
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

Robert Kolker wrote in message <6jelbm$...@news-central.tiac.net>...
> I think not. Countably infinite referes to the cardinality
> of a set of objects that can be put in one to one correspondence
> with the set of integers. Are there infinitely many of any
> kind of thing in the physical cosmos? I have seen no evidence
> to that effect.

What I refer to is that which the universe seems to have in common with the
set of integers, namely that no matter how much of it is explored there is
more.    The universe is continually expanding.   The realm of knowledge
seems to me to qualify as being infinite.  The amount to know is not finite.
 What error, if any, am I making?

Question:  Does the universe expand at the speed of light?   If not, then
how could a universe that is 15 billion years old that are that far away
from us?   At least it would have had to expand at half of light speed it
seems (perhaps naively) to me.

- samantha


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Bob Renninger  
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 More options 16 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: Bob Renninger <Rennin...@att.net>
Date: 1998/05/16
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

In article <6jht70$r0...@nntp2.ba.best.com>,
 "Samantha Atkins" <saman...@theLove.org> wrote:

>Question:  Does the universe expand at the speed of light?   If not, then
>how could a universe that is 15 billion years old that are that far away
>from us?   At least it would have had to expand at half of light speed it
>seems (perhaps naively) to me.

You have to be clear about what you mean by "the speed at which
the universe expands."  There is no boundary moving outward at some
speed.  In relativistic cosmologies, there is a "radius of curvature"
parameter (call it "a") for both open (spatially infinite) and closed
(spatially finite) universes.  The theories tell you the rate at which
"a" changes with time.  

One of my textbooks shows that in a typical model, "a" is proportional
to the 2/3 power of t.  

The formula for "a" depends on some parameters that are not readily
measured, but if you take the rate of change of "a" divided by "a",
(ie, (1/a)da/dt), you get none other than the Hubble constant, H, which
is roughly equal in magnitude to 1/(age of the universe).  H is computed
by dividing the recessional velocity of distant galaxies with their
distance from earth.

Bob Renninger

"Just Say No:  To Slogans."


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Bob Renninger  
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 More options 16 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: Bob Renninger <Rennin...@att.net>
Date: 1998/05/16
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

In article <6jehlb$c3...@nntp2.ba.best.com>,
 "Samantha Atkins" <saman...@theLove.org> wrote:

>Ah.  But at any particular time, T, after the Big Bang, the universe is
>guaranteed to be at a finite size.   This was all I was trying to assert.

Ah, but you are wrong.

Bob Renninger

"Just Say No:  To Slogans."


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Bob Renninger  
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 More options 16 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: Bob Renninger <Rennin...@att.net>
Date: 1998/05/16
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

In article <6jeibq$cb...@nntp2.ba.best.com>,
 "Samantha Atkins" <saman...@theLove.org> wrote:

>A question I don't know how to approach with my limited scientific
>knowledge:   In the infinite gravity well of a black hole wouldn't the
>acceleration due to gravity be infinite and thus would not velocities far in
>excess of a mere finite value like c, the speed of light,   be attainable?
>Just a curious question way too late at night.

No.  In relativity theory, velocities of material objects only approach
the speed of light, never reach it.  The energy can increase without
limit, but not the speed.  This is very well confirmed for small
objects, like the electrons in your TV's picture tube.

Bob Renninger

"Just Say No:  To Slogans."


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Jonathan Carryer  
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 More options 17 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: Jonathan Carryer <jcarr...@YorkU.CA>
Date: 1998/05/17
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

Bob,

>>Ah.  But at any particular time, T, after the Big Bang, the universe is
>>guaranteed to be at a finite size.   This was all I was trying to assert.
>Ah, but you are wrong.

Very clever comeback.  Now will someone PLEASE back up an assertion
with an argument?

*Jonathan


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Jonathan Carryer  
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 More options 17 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: Jonathan Carryer <jcarr...@YorkU.CA>
Date: 1998/05/17
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

Bob,

>You have to be clear about what you mean by "the speed at which
>the universe expands."  There is no boundary moving outward at some
>speed.  In relativistic cosmologies, there is a "radius of curvature"
>parameter (call it "a") for both open (spatially infinite) and closed
>(spatially finite) universes.  The theories tell you the rate at which
>"a" changes with time.  

Just to clarify, is this model sort of like blowing up a balloon that
has no outside?  That is, you don't actually add any space to the
universe, you just stretch the space that's already there?

*Jonathan


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T. Laird  
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 More options 18 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: "T. Laird" <tlla...@metro.net>
Date: 1998/05/18
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

Infinite has more than one definition, as do most words, e.g.:
infinite: not capable of definition, not countable
infinite: limited perhaps, but not countable by humans
infinite: pertaining to reified concepts that cannot, by their nature,
be limited, but
        which, also by their nature, cannot be said to describe anything real.

The middle definition is perhaps what we keep bumping up against. The
first and third
definitions are perhaps the ones that we confuse and refuse to admit
what we are doing.

But I really want to know, how did the objects near the present boundary
of the universe
(NOT THE BOUNDARY ITSELF, THE OBJECTS!) reach their position so that
they sent back
light which we are only now receiving, if at the time they sent the
light, they were
so much closer (to the center of the alleged big bang, and thus closer
to the material
that we are sitting on to observe from)?


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GRADinc  
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 More options 18 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: GRADinc <grad...@aol.com>
Date: 1998/05/18
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

T. Laird

>how did the objects near the present boundary
>of the universe ... reach their position so that
>they sent back
>light which we are only now receiving, if at the time they sent the
>light, they were
>so much closer (to the center of the alleged big bang, and thus closer
>to the material
>that we are sitting on to observe from)?

Say the object you are asking about is 10 billion light years away
and the big bang happened 15 billion years ago (to use
definite numbers).  
The light would we are now seeing from the object would
have been emitted 10 billions years ago when the universe
was 1/3 it's current size.  This sounds strange, I admit.
If at the time of emission we were only 3.3 biilion LY from
the object why did it take the light 10 billion  years to get
here?
The answer is that it an affect of red shift.  Now
and at the time of emission we would be traveling
2/3 of light speed relative to the object (slight variations
in speed depending on details of model universe, but
the essential point is not changed).  This makes it take
"3 times" as long for the light to get here as compared to
what it would take if the universe were not expanding.

That's as close as I can come in words today.  The details
are in the math and inasmuch as the math is logically axiomatic
it is consistent so there is not contradiction, only an apparent
contradiction when the facts of reality are expressed in
the langauge of English.  [Same point applies to my favorite
bugbear, the second definition of infinity you provided}

>infinite: limited perhaps, but not countable by humans

Tom Clarke

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Bob Renninger  
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 More options 19 May 1998, 08:00
Newsgroups: humanities.philosophy.objectivism
From: Bob Renninger <Rennin...@att.net>
Date: 1998/05/19
Subject: Re: Rand and Infinity (Was: Re: Rand & Von Neumann....)

In article <6jm1t4$r0...@sunburst.ccs.yorku.ca>,
 Jonathan Carryer <jcarr...@YorkU.CA> wrote:

>Just to clarify, is this model sort of like blowing up a balloon that
>has no outside?  That is, you don't actually add any space to the
>universe, you just stretch the space that's already there?

Yes, that's just about it.  The balloon has neiter an  outside or an
inside.  There is just the surface of the balloon, which behaves like
the surface of an ordinary balloon, and in particular, has no boundary.  
When it expands, you indeed stretch the space that's already there.

Bob Renninger

"Just Say No:  To Slogans."


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